' ' ' - m are the Question 1 in this question we begin by constructing a competrtwe market for a good, ant:i 2:335 (:1; some outcome when supply is controlled by a single-price monopolist. Suppose that the demand endiwre on a" beverage comes from households with the preferences over units of the beverage (x1) an exp other goods (x2) represented by the following utility function, U(I1,X2) = 800111031) '1' 1:2 I l ' I r e! Each household has an exogenous income of I per period. The second good Is referred to as a composnt good and is an amount of money. We assume throughout that p; = 1. i) (4 marks) Derive a household's ordinary demand functions, x1 (pl, 1, I) and x2 0-71, 1, 1') wife: :h: are price-takers in the market for the beverage. How large does the exogenous income nee o in order for the household to enjoy a positive amount of both 'goods'? If f ii) (2 marks) Suppose there are 80 househoids who participate in the market for the beverage. He 0 the households have an income of $1200 per period, and the other half have an income of $3000 per period. Find the market demand function for the beverage. iii)' (3 marks) The market is supplied by two types of rms with the following cost functions, 3 2 a _ .1. 2 (3\"(x) = 10.0003: and C (x) 10.000x . Find each type of rm's supply function if we treat them as price-takers. ' (2' marks) If there is one rm of each type, nd the market supply function using your answer In III). v] (2 marks) Calculate the market equilibrium price and quantity. vi) {2 marks) Use your answer in v) to find the profits of each firm type. vii) [3 marks) Illustrate the market equilibrium using a sketch. of the supply and demand functions. viii) (3 marks) if the market was instead supplied by a monopolist with the cost function 000 = 3 x2 . . ' M ' some . can you nd a prot maximizing choice of output? Explain. - ix) (2 marks) If the monopolist had the cost function (20:) = 40:00 15", but only discrete blocks of thousands of units of the good could be chosen {x =' U, 1000, 2000, 3000, ...)_by the monopolist, _ what amount would the monopolist supply then? Explain your reasoning. ' X) [3 marks) Compare the monopolist's prot maximizing choice in ix) to the market equilibrium you found in v) using a sketch with the market demand and relevant supply-side curves. Identify the deadweight loss (extent of inefciency) arising from the monopolist's restriction of supply to the market